"We’re asking our tech community for new takes on older technology, and inviting designs about how they might enhance the vitality of our public spaces,” Bloomberg said in the Tuesday announcement.

The city's current pay phone contract expires in 2014. There are more than 11,000 pay phones (compared to over 35,000 in the late 1990s) scattered throughout its five boroughs. In this digital age of smartphones and tablets, the pay phone earns NYC only about $18 million every year, noted the New York Post.

But after Hurricane Sandy knocked out cellular service in parts of Manhattan in late October, residents flocked to pay phone kiosks to make calls.

"Phones that normally do two dollars a day are taking in $50 a day," said Peter Izzo of pay phone-operating franchise Van Wagner Communications, to the Wall Street Journal. "In times of distress, the people of the city love them."

Mayor Bloomberg said while the current coin-operated pay phone is handy during emergencies, "to thrive, the payphone of the future needs to offer valuable services at all times."

The competition's deadline is Feb. 18 and up to 15 entries (physical or virtual prototypes) will be selected for a March 5 demonstration at Quirky's New York headquarters. Judges include Betaworks CEO John Borthwick and former U.S. Deputy CTO Beth Noveck.

In the most recent attempt to modernize its pay phones, the city rolled out a pilot program with start-up City 24/7 to install "SmartScreens" in 250 old phone booths--the 32-inch touch screens made their debut in Union Square, the New York Times reported.